The Natural/Non-Natural Distinction

Lewis's “New Work for a Theory of Universals”
(1983b) contains by far his most extensive treatment of both the nature
of and need for a distinction between perfectly natural properties and
relations, and less-than-perfectly natural properties and relations.
Presupposing his realism about possible worlds, Lewis argues that for
any set of actual and possible objects (fundamental or not),
there is a property, namely the property an object has just in case it
is a member of the given set. Likewise, for any set of ordered pairs of
actual and possible objects, there is a two-place relation; and so on.
(Note that since the objects can themselves be sets, the
position automatically makes room for higher-order properties and
relations.) In fact, he goes further, taking properties and relations
simply to be such sets.

This position is roughly analogous to the position that to every
predicate, no matter how oddly defined, there corresponds a property or
relation; and likewise to the position that to every method we might
conceive of for classifying objects (or object-tuples), no matter how
unprincipled, arbitrary, and gerrymandered, there corresponds a
property (or relation). The analogy breaks down only because our
linguistic devices and conceptual resources are far too limited to
encompass all the classifications (i.e., sets of possibilia)
there are. (And also because some of our predicates are logically
pathological, so that there is no such thing as the set of possibilia
that satisfy them. Consider the old standby, “— is a set
that is not a member of itself”.) Properties and relations, on
this conception, are abundant—to put it mildly.

Lewis argues that properties and relations, on this abundant
conception, are well-suited to play the roles of semantic values in
formal linguistics, and contents for mental states. But even if he is
right, it would be a mistake to see him as offering here an argument
for believing in the sorts of things that, on the abundant
conception, are to be called “properties” and
“relations”. It's not that he's averse to
arguing that we should believe in X's because doing so will make
our theoretical lives easier. (See the forthcoming article on his
theory of metaphysical modality for discussion of his most famous (or
notorious!) such argument, in support of his modal realism, presented
most comprehensively in his 1986e.) It's rather that his realism
about possible worlds, combined with his realism about set theory,
makes it inevitable that he is committed to the existence of
these entities. The issue for him is a rather more modest one: he
already believes in certain entities, which he finds, happily enough,
will do a certain sort of theoretical work for him; given the work in
question, he finds it appropriate to call these entities
“properties” and “relations”. Observe that
matters are quite otherwise for those metaphysicians who don't
believe in Lewis's possible worlds; endorsing the abundant
conception will, for such a philosopher, likely require
carving out room in her ontology for them. (See Plantinga 1976 for an
example of one who makes use of the abundant conception against a quite
different ontological background from Lewis's.)

Now for the crucial point: the central argument of “New
Work” is that the abundant conception is badly inadequate, for a
wide range of theoretical tasks for which properties and relations are
needed. To cite two of the most obvious, suppose we wish to say that an
object changes over a given time interval just in case it
either gains or loses a property in that interval; or that two objects
are similar to the extent that they share properties. Equipped
only with the abundant conception, we will be left with the
trivializing conclusions that everything always (and necessarily)
changes, and that any two objects are just as similar as any other two.
That seems wrong: it seems, by contrast, that these accounts of change
and of similarity must presuppose a much more discriminating conception
of what counts, in the relevant sense, as a property.
Lewis's statement of the point is characteristically elegant:

Because properties are so abundant, they are undiscriminating. Any
two things share infinitely many properties, and fail to share
infinitely many others. That is so whether the two things are perfect
duplicates or utterly dissimilar. Thus properties do nothing to capture
facts of resemblance. …Likewise, properties do nothing to
capture the causal powers of things. Almost all properties are causally
irrelevant, and there is nothing to make the relevant ones stand out
from the crowd. Properties carve reality at the joints—and
everywhere else as well. If it's distinctions we want, too much
structure is no better than none. (1999, p. 13)

“New Work” goes on to extend the list of jobs for which
the abundant conception is inadequate: Lewis argues that his accounts
of supervenience, lawhood, causation, events, and mental content all
provide essential work for a theory of properties and relations that
conceives them as vastly more sparse than does the abundant
conception.

For present purposes, it will pay to focus on an additional, and
central, piece of “work” (not singled out for attention in
“New Work”; though see Lewis 2001). It is the basic
job-description articulated in the main text, the one highlighted by
our two foundational metaphysical questions: What is there? What is it
like? Almost-Lewis, remember, answers the first by saying that what
exists (fundamentally) are spacetime points. But it seems that it will
not do to say that what they are like is entirely settled
merely by the various sets that can be composed out of them.
Tim Maudlin has put the point nicely: “if there are no objective
facts about the comparative character of objects, we must fall back
into the unpalatable position that the only real structure of the
universe is its cardinality.” (1997, p. 84) Rather, what they are
like—in the relevant and fundamental sense—is
settled by what perfectly natural properties and relations they
instantiate.

Two additional points deserve mention. First, Lewis's account
of modality provides him, at least, with an additional and
crucial piece of “work” for a theory of natural properties
and relations. For he holds that reality as a whole divides into chunks
that deserve to be called “possible worlds”; the central
idea behind his reduction of the modal to the non-modal is that modal
idioms involve, in a certain systematic way, quantification over these
chunks and the things they contain. (See the forthcoming companion
article for details.) Some account is needed, then, of how the chunking
works—of what it is for two things to belong to the same possible
world. Lewis's favored answer appeals to the one species of
perfectly natural relation that he is sure that there is:
spatiotemporal relations. Thus, two things are world-mates, according
to him, iff they bear some spatiotemporal relation to each other. (See
Lewis 1986e, esp. pp. 69ff.)

The second point concerns the need for a graded distinction
between more and less natural properties, and what sort of account of
natural properties can meet this need. Now, this need does not
arise from what I have been emphasizing as the foundational role for a
natural/non-natural distinction, which is to secure a clear and
objective sense in which reality as a whole can be said to have a
fundamental structure. But for Lewis, it does arise all the
same, perhaps most dramatically in his account of how our talk, and
especially thought, manages to have reasonably determinate
content (Lewis 1983b, 1984). The companion article on his
applied metaphysics takes up this issue in more detail, but for now
suffice it to say that an essential part of what makes it the case that
we refer, in thought (and hence, for Lewis, in talk) to certain
properties and entities, and not to others that in purely formal
respects would make equally good candidates, is that the former
properties and entities are more objectively eligible as
candidates for reference than the latter; and this graded distinction
of eligibility is in turn to be explained in terms of a graded
distinction of naturalness.

Given Lewis's reductionist commitments, he therefore needs
some account of how the facts about the pattern of instantiation of
perfectly natural properties make it the case that among those
properties that are not perfectly natural, some are
nevertheless more natural than others (whence by extension, we
can hope, some non-fundamental entities will count as “more
natural” than others). He says very little about this issue, but
the account he evidently favors gets hinted at occasionally—for
example, here, in “Putnam's paradox”:

… physics discovers which things and classes are the most
elite of all; but others are elite also, though to a lesser degree. The
less elite are so because they are connected to the most elite by
chains of definability. Long chains, by the time we reach the
moderately elite classes of cats and pencils and puddles; but the
chains required to reach the utterly ineligible would be far longer
still. (1999, p. 66)

This suggests the following proposal: Property F counts as
more natural than property G just in case some predicate
expressing F can be defined, in terms of predicates
expressing perfectly natural properties, more simply than can any
predicate expressing G.

It seems a difficult, important, and entirely open question whether
this proposal succeeds—and if not, what else might replace
it.